New Comic Book About Logic, Math, and Madness 99
areYouAHypnotist writes to tell us the New York Times has the scoop on a new comic book about the quest for logical certainty in mathematics. "The story spans the decades from the late 19th century to World War II, a period when the nature of mathematical truth was being furiously debated. The stellar cast, headed up by Bertrand Russell, includes the greatest philosophers, logicians and mathematicians of the era, along with sundry wives and mistresses, plus a couple of homicidal maniacs, an apocryphal barber, and Adolf Hitler."
Um... (Score:2, Insightful)
That follows only if you think that the logicist system for the foundation of mathematics proposed in the Principia is something "similar" to Fortran and the calculus.
It's the axioms... (Score:5, Insightful)
All (correct) mathematical proofs are true, if the axioms are true. However, there's an infinite set of axioms and the only reason you have to believe any of them correspond to the system you are trying to predict is through observation. If you don't have any observations, if you're trying to make a priori knowledge, then your prediction power is thus infintesimal. Or in English, you don't know shit. As for pure mathematics, imagine it a little bit like infinite quantum universes in sci-fi. For every mathmatical result there are other sets of axioms leading to all other possible results. Without excluding axioms you can not exclude any results, so you're only going in circles defining your own results. In English, anything's possible.
Of course in practice you would have to create insane and arbtrary axioms to do this. But "logical" axioms like the set of real numbers or three dimensional space only appear so because of observation and how it reflects the real world. A priori you have no basis to say why one set of axioms should better reflect reality than the other. So I would say the answer is simply false, you can not have meaningful mathematics without context. However, once you do have meaningful axioms through observation you can get many results through mathematics that are non-obvious through observation. Honestly though, you're more heading into philsophy than mathematics once you go that deep.
Re:The ending of the strip is rather disappointing (Score:5, Insightful)
Agreed. The problem is you get philosophers that write books about mathematics and physics. They almost always get everything wrong or blow things out of proportion. Things philosophers love to talk about without actually knowing anything about them: quantum physics, logic (especially Godel's Theorems), set theory.
Re:The ending of the strip is rather disappointing (Score:3, Insightful)
Re:Maybe it's just an unfortunate quote, but... (Score:2, Insightful)
Re:wrong similarity (Score:1, Insightful)
Except that this is a historical drama (and perhaps comedy), not an instructional text.
Re:Maybe it's just an unfortunate quote, but... (Score:1, Insightful)
Ask anybody on the street to name even one mathematician of either sex.